* Shares supported by optimism on earnings, global growth
* Investors look to Fed chief choice, U.S. tax debate
* Oil prices firm on output cut extension
* Bitcoin hits record after CME says will launch futures
TOKYO, Nov 1 (Reuters) - Asian shares looked set to extend their gains into a fourth straight day on Wednesday on the back of solid economic growth, while oil prices were on a bull run on hopes of an extension of output cuts by major oil producers.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.3 percent in early trade while Japan's Nikkei gained 1.0 percent.
Wall Street's three major indexes ticked up on Tuesday to end October with their biggest monthly gains since February.
Markets showed a muted response after a pickup truck driver killed eight people and injured more than a dozen others by driving down a New York City bike path, an incident U.S. authorities said was a terrorist attack.
Investors are focused on the progress of a U.S. tax-cut plan being developed by President Donald Trump and fellow Republicans and on Trump's announcement of the next head of the Federal Reserve. The White House said he will reveal his Fed pick on Thursday.
Tax legislation had been expected on Wednesday, but sources said Republicans in the U.S. House of Representatives will delay the release for a day as lawmakers try to overcome differences involving the treatment of retirement savings accounts and state and local taxes.
"If the negotiation gets derailed, that would have a negative impact on markets so we need to be careful," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management.
Trump's decision on the Fed chair is upstaging the start of its two-day policy meeting in Washington on Tuesday, although it is widely expected to leave interest rates unchanged in its statement on Wednesday.
Trump is likely to pick Fed Governor Jerome Powell, who is seen as more dovish on interest rates and thus relatively stock market friendly, sources have told Reuters.
Expectations that Powell will lead the Fed have helped to drive down U.S. bond yields and the dollar this week.
The dollar's index against a basket of six major currencies eased to 94.62 from last week's three-month peak of 95.15 .
The euro was little moved at $1.1650, though it kept some distance from its three-month low of $1.1574 touched on Friday after the European Central Bank's stance was perceived to be more dovish than expected.
The dollar fetched 113.76 yen, off Friday's high of 114.45 yen.
The biggest mover in early Wednesday trade was the New Zealand dollar, which jumped 0.7 percent to $0.6893 after the country's jobless rate sank more than expected to a nine-year low of 4.6 percent.
Bitcoin hit another record high after CME Group Inc, the world's largest derivatives exchange operator, said on Tuesday it will launch a futures contract for bitcoin later this year, marking a major step in the digital currency's path toward legitimacy.
Oil prices extended their rally which began in early October, largely driven by hopes that oil producing countries will agree to extend output cut at their meeting the end of this month.
Brent crude futures hit a two-year high of $61.41 per barrel on Tuesday and stood at $61.16 per barrel in early Asia trade, up 0.4 percent on the day.
U.S. crude futures held at $54.87 per barrel, near its eight-month high of $54.85 hit on Tuesday.
(Editing by Kim Coghill)